Final answer:
To find the general solution given y1 satisfies the complementary equation, we use the method of variation of parameters. We find the second linearly independent solution y2 and express the solution using the general solution formula.
Step-by-step explanation:
To find the general solution given y1 satisfies the complementary equation with the given differential equation, we will use the method of variation of parameters. First, we need to find the second linearly independent solution y2. Then, using the formula for the general solution, we can express the solution in terms of y1 and y2.
Let's start by finding y2. Assuming y2 takes the form y2 = u(x)y1, we substitute this into the given differential equation and solve for u(x). After finding y2, we can use the formula for the general solution: y = c1y1 + c2y2, where c1 and c2 are constants.
In this case, y1 = √x. To determine y2, we substitute y2 = u(x)√x into the differential equation and solve for u(x).
After finding y2, we can write the general solution as y = c1√x + c2y2.